Which represents the inverse of the function f(x) = 4x?

Answer:

- 2, 7 , - 8

Step-by-step explanation:

substitute the given values of x into the expression

(a)

x = 0 : 3(0) - 2 = 0 - 2 = - 2

(b)

x = 3 : 3(3) - 2 = 9 - 2 = 7

(c)

x = - 2 : 3(- 2) - 2 = - 6 - 2 = - 8

Answer: 3/4 of a gallon

Step-by-step explanation:

1/4 times 1/3 is 3/4 so she would need to buy a gallon of paint

[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \left( 4^{\frac{2}{5}} \right)^{\frac{1}{4}}\implies 4^{\frac{2}{5}\cdot \frac{1}{4}}\implies 4^{\frac{1}{10}}\implies \sqrt[10]{4^1}\implies {\Large \begin{array}{llll} \sqrt[10]{4} \end{array}}[/tex]

Answer:46kg

Step-by-step explanation:

23+2=25

50/25=2

2x23=46kg

Answer:

46 kg

Step-by-step explanation:

Ratio of copper to tin in the bronze alloy is 23:2

That means, as a ratio of the entire brass mass, the copper content is in the ratio of 23/(23 + 2) = 23/25

Since the mass of the bronze statue is 50 kg, the mass of copper in it must be 50  x  23/25 = 46 kg

The remaining kg (2/25 of 50 kg) is tin

Answer: Yes, because 4 + 5 > 8

Step-by-step explanation: The sum of 4 + 5 must be more than 8 to be a triangle

Answer:

The answer is A) Yes, because 4 + 5 > 8

Step-by-step explanation:

I got it right loves <3

Answer:

[tex]y=-\frac{1}{4}x+2[/tex]

Step-by-step explanation:

Perpendicular lines have slopes thst are negative reciprocals, so the slope of the line to be found is -1/4.

Substituting into point-slope form, the equation is [tex]y-4=-\frac{1}{4}(x+8)[/tex].

Rearranging into slope-intercept form,

[tex]y-4=-\frac{1}{4}(x+8) \\ \\ y-4=-\frac{1}{4}x-2 \\ \\ y=-\frac{1}{4}x+2[/tex]

Mark receives a scale report and on the Math section, he earned a raw score of 39 which is at the 68th percentile, meaning that the total raw score on the Math section is 57

Find out the total score of the Math score, 100th percentile

     Given; raw score- 39 which is at the

                       68th- percentile

For someone to be at the 100th percentile, he or she must have scored all the questions right.

In Mark's case, he had a score of 68 percentile with a score of 39

Total raw score for the Math section;

    state;   If score of 39 = 68 percentile

                          ?                 100 percentile

Cross multiply to solve for the unknown

Thus;  39 * 100 / 68

         =  57

Therefore, total raw score on the Math section is 57, which is at the 100th percentile.

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The rational numbers - 5 / 6 and - 7 / 10 are equivalent to - 25 / 30 and - 21 / 30, respectively. Then, the relationship is that - 5 / 6 is the less than - 7 / 10 as - 25 < - 21.

Rational numbers are real numbers of the form m / n, where m and n are integers and n is not zero. In this problem we need to determine the relationship between two rational numbers, this can be done by amplifying the two rational numbers to a form with the same denominator and then compare the two numerators.

First, find the least common multiple of the two denominators:

6 = 2 × 3

10 = 2 × 5

L.C.M. = 2 × 3 × 5 = 30

Second, amplify each rational number:

- (5 × 5) / (6 × 5) = - 25 / 30

- (7 × 3) / (10 × 3) = - 21 / 30

Third, compare the numerators of the fraction found in the previous step:

Since - 25 < - 21, then - 5 / 6 < - 7 / 10.

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Answer:

[tex]{ \tt{ - \frac{1}{6} = \frac{f - 3}{7 - 1} }} \\ \\ { \tt{6(f - 3) = - 6 }} \\ \\ { \tt{f - 3 = - 1}} \\ \\{ \tt{f = 2}}[/tex]

Answer:-2

Step-by-step explanation:

Answer:

166,460 doctors registered.

Step-by-step explanation:

32.2% -------- 53,600 female doctors

100% --------          X

X * 32.2% = 100% * 53,600

X = (100% * 53,600) / 32.2%

X = 166,460 doctors

The most appropriate choice for LCM will be given by

Smallest number of gift boxes Katy can fill is 56

What is LCM?

Suppose a and b are two numbers. LCM of a and b is the lowest common multiple of a and b. LCM of a and b is the lowest number that is divisible by both a and b.

Here,

Katy buys toys in bags of 8.

Katy buys keyrings in bags of 14.

Each gift box will contain one toy and one keyring.

Number of gift boxes Katy can fill has to be a common multiple of 8 and 14

Smallest number of gift boxes Katy can fill is the least common multiple of 8 and 14

Now,

8 = 2 x 2 x 2

14 = 2 x 7

LCM of 8 and 14 = 2 x 2 x 2 x 7

                           = 56

Smallest number of gift boxes Katy can fill is 56

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g(x)×h(x) means we will have to multiply the two functions.

[tex]g(x) \times (h(x) = (3 {x}^{2} - 1)( {x}^{2} - x) \\ = 3 {x}^{2} ( {x}^{2} - x) - 1( {x}^{2} - x) \\ = 3 {x}^{4} - 3 {x}^{3} - {x}^{2} + x \\ g(x) \times h(x) = 3{x}^{4} - {x}^{3} - {x}^{2} + x[/tex]

ATTACHED IS THE SOLUTION

The value of x is 6 and the measure of angle LJK is 27°.

According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.

We have the measure of the following angles,

m∠JKL = ( 3x - 16 )°

m∠LJK = ( 2x + 15 )°

m∠KLM = ( 8x - 19)°

In ΔJKL, JL is extended through point L to point M.

At point L, the measure of angle JLK will be as,

m∠KLM + m∠JLK = 180°

m∠JLK = 180° - m∠KLM

m∠JLK = 180° - ( 8x - 19)°

m∠JLK = ( 199 - 8x )°

Now,

In triangle JKL,

By angle sum property:

m∠JKL + m∠LJK + m∠JLK = 180°

(3x – 16)° + (2x + 15)° + ( 199 - 8x )° = 180°

- 3x + 198 = 180

- 3x = - 18

x = 6°

Therefore,

m∠LJK = ( 2x + 15 )°

m∠LJK = ( 2(6) + 15 )°

m∠LJK = ( 12 + 15 )°

m∠LJK = 27°

The measure of angle LJK is 27°.

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Answer:

<KLC

Step-by-step explanation:

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.

Both are obtuse angles and are on the opposite side of the transversal line

Answer:

∠KLC is the alternate angle of ∠BKL

Step-by-step explanation:

Alternate angles are angles that are opposite of one another and on two different parallel lines created by an intersecting line (also known as a transverse line).

In this case, the parallel lines are lines A↔B and C↔D, and the transverse line is M↔N. Therefore, the alternate angle from ∠BKL is ∠KLC.

The equation of the line in the slope-intercept form is y = -1/4x + 9

From the question, we are to determine the equation of the line that passes through the given points.

The given points are (-4, 8) and (4, 6)

Using the formula,

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

x₁ = -4

y₁ = 8

x₂ = 4

y₂ = 6

Thus,

(y - 8)/(x - -4) = (6 - 8)/(4 - -4)

(y - 8)/(x + 4) = -2 / (4 + 4)

(y - 8)/(x + 4) = -2 / 8

(y - 8)/(x + 4) = -1/4

4(y - 8) = -1(x + 4)

4(y - 8) = -x + 4

y - 8 = -1/4x + 1

y = -1/4x + 1 + 8

y = -1/4x + 9

Therefore,

The equation is y = -1/4x + 9

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Answer:

1. 4

2. 2

3. 35

4. 96

Step-by-step explanation:

1. (6-2)÷4=4

2. 18÷(2+7)=2

3. (11-4)×5= 35

4.(4+2+6)×8= 96

Answer:

1. 1

2. 2

3. 35

4. 96

For the above question, statement 2 and 4 are true for the given data and after plotting the dot plot and histogram.

As per the question statement, data is showing the number of pieces of mail delivered to a single home address each day for three weeks.

Which is as follows: 4, 0, 2, 6, 1, 0, 3, 4, 0, 2, 4, 1, 5, 2, 3, 1, 1, 2

10 for 3 days, 1 for 4 days, 2 for 4 days, 3 for 2 days, 4 for 3 days, 5 for 1 day and 6 for 1 day.

Statement 1: False because the number line of a dot plot would start at 0.

Statement 2: True

Statement 3: False as it should be 0, 1, 2, 3, 4, 5 and 6

Statement 4: True

Statement 5: False as it should show 3 bars at 0 in histogram

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Answer:

b,d

Step-by-step explanation:

The option that results in a graph that shows exponential decay is Option(b) f(x) = 3(0.7)ˣ.

According to the question, we have to determine the function that results in a graph that shows exponential decay.

The function will show an exponential decay if the value of b was less than 1 and greater than 0.

As we can notice in the second option, f(x) = 3(0.7)ˣ, where b is equal to 0.7 which is less than one.

So, f(x) = 3(0.7)ˣ shows exponential decay.

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The complete question is: "Which of the following options results in a graph that shows exponential decay?

a. f(x) = 0.6(2)ˣ

b. f(x) = 3(0.7)ˣ

c. f(x) = 0.4(1.6)ˣ

d. f(x) = 20(3)ˣ."

Answer:

A

Step-by-step explanation:

Do long division. See the attached image for work.

Answer:

B

Step-by-step explanation:

[tex]\frac{56}{90}[/tex]

= 56 ÷ 90

= 0.6222222..

= 0.62 ( with a bar above the 2 , indicating the 2 is repeating )

Answer:

65 feet

Step-by-step explanation:

[tex]3705=57h \\ \\ h=\frac{3705}{57}=65[/tex]

The equation intercept at (2,3) in the graph given in the question.

Given two equations are ,

3 x - y = 3

-3 x - y = -9

to solve the equations, substract both equations ,

(3 x - y = 3) - (-3x -y = -9)

we get,  6x =12

              x = 2

by substituting value of x in any of the equation we get ,

3 x 2 -y =3

6 -y =3

-y = -3

y = 3

so x = 2 , y = 3

the points on the graph is (2,3)

Both equations are in slope intercept form.

The graph of y = mx +b, where m is the slope and b is the y intercept, is shown below.

They have the same y intercept, so they cross at (2,3).

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Answer:

62.5

Step-by-step explanation:

Answer: One seventh of the sum of 19: 2.714

Product of 4 and 11: 44

Step-by-step explanation:

4x11=44

One seventh times 19 equal 2.714.

1/7 x 19/1 = 19/7

Simpified 2 5/7

2 5/2 as decimals is 2.714

Step-by-step explanation:

we sadly need to do all the multiplications for the whole polynomial in standard form.

the other 3 things we get out of the given form :

we multiply 3 terms, each in x. the result will be x³.

so, we have the 3rd degree.

the leading coefficient is 1, as for the x³ term we get x×x×x = x³. no other number is involved.

the constant term is the extreme on the other end. it is 4×2×1 = 8.

so, now for the full multiplications, that should also show you, why I could make the conclusions above.

(x+4)(x-2)(x+1)

we do this by multiplying first 2 terms with each other, and then we multiply that result by the third term.

remember, we need to multiply every item of one term with every item in the other term.

(x+4)(x-2) = x² -2x + 4x - 8 = x² + 2x - 8

now

(x² + 2x - 8)(x+1) = x³ + x² + 2x² + 2x - 8x - 8 =

= x³ + 3x² - 6x - 8

so, that is already the standard form

f(x) = x³ + 3x² - 6x - 8

The table with the situations that represent or not proportional relationships of distance and time is given at the end of the answer.

A situation represents a proportional relationship if the output variable y in the y-axis is written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:

y = kx.

One example, in the context of this problem, is the relation between velocity, distance and time, as velocity is distance divided by time, hence:

v = d/t.

The relation between distance and time is given as follows:

distance = velocity x time

distance = v x t.

Hence it will only be proportional if the velocity is constant, that is, if the acceleration is of zero.

Examples of non-proportional situations in the context of this problem are:

The distance and time table (4 - 15, 8 - 30, 12 - 45) does not show enough information, we need to know if the initial point was of (0,0).

The objects are missing, and have been dragged to their correct situation on the table.

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Answer:

3.375

3[tex]\frac{375}{1000}[/tex]

[tex]\frac{27}{8}[/tex]

Step-by-step explanation:

The first answer divide 81 by 24 and you will get the decimal answer of 3.375.

0.375 is [tex]\frac{375}{1000}[/tex]

[tex]\frac{81}{24}[/tex]  Divide the top and the bottom by 3 to get [tex]\frac{27}{8}[/tex]

The slope of the function as a unit rate for the linear situation. y = [tex]-4\frac{4}{5}[/tex]x + [tex]13\frac{1}{2}[/tex] can be viewed as [tex]-4\frac{4}{5}[/tex] by taking the derivative of the first term of the equation.

The slope m=y/x of a straight-line y=mx+b quantifies the change in y for every unit change in x. This can also be interpreted as a kind of measure of "sensitivity''.

Finding the slope of a function is like finding the rate at which the value of y (the dependent variable) changes in relation to x is what this method entails (independent variable).

To find the slope of a line that is given with the equation of the line, first you have to write the equation of the line in a slope-intercept form.

Then use inverse operations in order to solve for y so that it is written as y=mx+b. Thereafter you can easily spot the slope since the slope is the coefficient of the x variable, or in other words, the number in front of x.

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Answer: The price of the apartment lies in the range of $1300 to $1800

Step-by-step explanation: Because Carlos doesn't exactly know how much  he'll make at his new job but he knows the range will be between 3000$ and 4000$ we will use inequality to solve this problem.

Let the rent on the new apartment = r

let monthly pay of Carlos = x

Given, apartment related fees = 200$

Given he is willing to use half of his monthly pay for rent and apartment related fees combined.

∴rent + apartment related fees = Monthly pay / 2

⇒[tex]r + 200 = \frac{x}{2}[/tex]

⇒[tex]x=2*(r+200)[/tex]

⇒[tex]x=2r+400[/tex]                                                (1)

Given Carlos' monthly pay is in the range of $3000 to $4000

∴[tex]3000\leq x\leq 4000[/tex]

⇒[tex]3000\leq (2r+400)\leq 4000[/tex]                             (from equation (1))

⇒[tex]3000-400\leq 2r+400-400\leq 4000-400[/tex]     (subtracting 400)

⇒[tex]2600\leq 2r\leq 3600[/tex]

⇒[tex]\frac{2600}{2}\leq \frac{2r}{2}\leq \frac{3600}{2}[/tex]                                           (dividing by 2)

⇒[tex]1300\leq r\leq 1800[/tex]                                           (2)

ANS: The apartment lies in the price range of $1300 to $1800 as given by equation (2)

here is a problem solved using inequality

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The percentage of money spent on books to that of cost for last semester is 16%

The cost for last semester was 2000.

The cost books was 320.

The percentage formula = part/whole × 100

Part = 320

Whole = 2000

Equation = 320/2000× 100

               = 32/20

               = 16%

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